This class is divided in three parts and will cover hydrodynamics of passive fluids, hydrodynamics of active fluids, and biological pattern formation processes. We will review basics of continuum mechanics and equilibrium and non-equilibrium thermodynamics, linear response theory, Onsager Relations, and the derivation of hydrodynamic equations both from microscopic rules and from a phenomenological approach using broken symmetries and conservation laws. Topics for passive fluids include thin film fluids and the statics and dynamics of nematic liquid crystals. Topics for active fluids include active nematic or polar fluids and biological fluids. Moving beyond linear response we will discuss spatial chemical systems, bifurcation theory, and biological pattern formation. The class will end on coupled chemical and hydrodynamic pattern formation processes relevant for morphogenesis.